0.119cm/s is the radius of the balloon increasing when the diameter is 20 cm.
<h3>How big is a circle's radius?</h3>
The radius of a circle is the distance a circle's center from any point along its circumference. Usually, "R" or "r" is used to indicate it.
A circle's diameter cuts through the center and extends from edge to edge, in contrast to a circle's radius, which extends from center to edge. Essentially, a circle is divided in half by its diameter.
dv/dt = 150cm³/s
d = 2r = 20cm
r = 10cm
find dr/dt
Given that the volume of a sphere is calculated using
v = 4/3πr³
Consider both sides of a derivative
d/dt(v) = d/dt( 4/3πr³)
dv/dt = 4/3π(3r²)dr/dt = 4πr²dr/dt
Hence,
dr/dt = 1/4πr².dv/dt
dr/dt = 1/4π×(10)²×150
dr/dt = 1/4π×100×150
dr/dt = 0.119cm/s.
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Answer: 
Explanation:
Given
Volume of air 
Temperature of air 
Increase in temperature 
Specific heat for diatomic gas is 
Energy required to increase the temperature is
![\Rightarrow Q=nC_pdT\\\\\Rightarrow Q=n\times \dfrac{7R}{2}\times \Delta T\\\\\Rightarrow Q=\dfrac{7}{2}nR\Delta T\\\\\Rightarrow Q=\dfrac{7}{2}\times \dfrac{PV}{T}\times \Delta T\quad [\text{using PV=nRT}]](https://tex.z-dn.net/?f=%5CRightarrow%20Q%3DnC_pdT%5C%5C%5C%5C%5CRightarrow%20Q%3Dn%5Ctimes%20%5Cdfrac%7B7R%7D%7B2%7D%5Ctimes%20%5CDelta%20T%5C%5C%5C%5C%5CRightarrow%20Q%3D%5Cdfrac%7B7%7D%7B2%7DnR%5CDelta%20T%5C%5C%5C%5C%5CRightarrow%20Q%3D%5Cdfrac%7B7%7D%7B2%7D%5Ctimes%20%5Cdfrac%7BPV%7D%7BT%7D%5Ctimes%20%5CDelta%20T%5Cquad%20%5B%5Ctext%7Busing%20PV%3DnRT%7D%5D)
Insert the values
